Observatories at universities are being particularly hard hit. Private endowments can stretch only so far, says Peter B. Boyce, executive officer of the American Astronomical Society in Washington. The costs of research have risen dramatically. Every advance farther into space demands ever more complex, expensive technology, he says.

Part of the reason for the lower budget is a trend away from support for science and its long-term goals, says -Geoffrey Burbidge, director of the Kitt Peak National Observatory in Arizona.

The flight of the Soviet satellite Sputnik in 1957 generated a great enthusiasm for science in the public and gave it a boost in the '50s and '60s, he continues. But now interest is flagging.

In the last four years, a quarter to a third of the US astronomy program has been lost to fund cutbacks, Dr. Boyce says. Of course, visible projects like the Space Telescope remain. But university research, the driving force for the future of astronomy, is shrinking because of this faltering support, he says.

The Reagan administration calls the Space Telescope an alternative to cutbacks on the ground. (Currently, a space shuttle is scheduled to put it into orbit in 1985.)

Dr. Boyce counters that the Space Telescope is still but one instrument, that its greatest contributions can best be made in the ultraviolet range which ground telescopes can't observe, and that, at slightly less than 100 inches in size, it's much smaller than the largest Earth-based telescopes. Major breakthroughs often come through large new telescopes, but the follow-up work requires a network of smaller facilities, he says.

The budget impact can be clearly viewed at southern Arizona's Kitt Peak observatory, one of the world's largest.

Director Burbidge says more than $1 million of Kitt Peak's $12.2 million budget was cut in February. Two 16-inch telescopes have been closed down and the use of other telescopes has been restricted.

Eighteen people have been let go, and 15 currently unfilled positions ''are no longer open,'' according to Dr. Burbidge. Since 1980 the observatory has lost 25 percent of its budget and 20 percent of its personnel.

Meanwhile, funds for the government-run infrared telescope atop Mauna Kea, an Hawaiian volcano, have been cut from NASA's budget. Scientists on that project call the withdrawal of funds ''an enormous waste,'' and ''unbelievable.''

Kitt Peak, atop the Quinlan Mountains southwest of Tucson, is ''a small city on a mountain top'' devoted to science, says Burbidge.

Despite the monetary pinch, the work of observatories goes on. For instance, Kitt Peak scientists are currently developing new techniques for building the reflecting mirrors central to optical telescopes. Mirror size has been limited by the fragility of glass and the distortions caused by a mirror. At present, the biggest usable mirror is approximately 200 inches in diameter, the size of the mirror in the telescope at Mount Palomar in California.

The new technology will permit construction of an enormous mirror that, instead of being a single piece, will be built out of fragments of mirrors. It will provide a reflective surface equal to that of a 600-inch mirror.

Other scientists are using Kitt Peak's solar telescope to study the effect of man's activities on the ozone layer of Earth's atmosphere and the return of Halley's comet in 1986.

These projects have not been hurt by this year's budget cuts, but Burbidge is not optimistic about the future. The cuts will continue and each cut will force more telescopes to be closed, more personnel to be let go, he says.

In spite of the Reagan administration's budget-cutting policy, Burbidge says he doesn't blame any one president.

''It didn't start with this administration, and it won't end with it,'' he says. ''It's been six or seven years since funds (for science) have kept up with inflation.''